ASPxGridView does not save a focused row in cookies. However, you can add this capability by saving and restoring a focused row index to cookies manually:
[JScript]function OnFocusedRowChanged(s, e){ ASPxClientUtils.SetCookie(s.name + '_focudedIndex', s.GetFocusedRowIndex());}function OnInit(s, e){if(ASPxClientUtils.GetCookie(s.name + '_focudedIndex') != null) s.SetFocusedRowIndex(ASPxClientUtils.GetCookie(s.name + '_focudedIndex'));}